Geodesic
Rings of Quotients of Rings of Derivations
Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 383-398

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The concept of a rational extension of a Lie module is defined as in the associative case [1, pp. 81 and 79]. It then follows from [3, Theorem 2.3] that any Lie module possesses a maximal rational extension (a rational completion), unique up to isomorphism. If now L and K are Lie rings with L⊆ K, we call K a (Lie) ring of quotients of L if K, considered as a Lie module over L, is a rational extension of the Lie module LL. Although we do not know if for every Lie ring L its rational completion can be given a Lie ring structure extending that of L (as is the case for associative rings), this is so, in any case, for abelian Lie rings (Propositions 2 and 4). 
Kleiner, Israel. Rings of Quotients of Rings of Derivations. Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 383-398. doi: 10.4153/CMB-1968-044-5
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     author = {Kleiner, Israel},
     title = {Rings of {Quotients} of {Rings} of {Derivations}},
     journal = {Canadian mathematical bulletin},
     pages = {383--398},
     year = {1968},
     volume = {11},
     number = {3},
     doi = {10.4153/CMB-1968-044-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-044-5/}
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